/**
* Copyright (C) 2009 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.math.differentiation;
import static org.testng.AssertJUnit.assertEquals;
import org.testng.annotations.Test;
import com.opengamma.analytics.math.function.Function1D;
import com.opengamma.analytics.math.matrix.DoubleMatrix1D;
import com.opengamma.analytics.math.matrix.DoubleMatrix2D;
import com.opengamma.util.test.TestGroup;
/**
* Test.
*/
@Test(groups = TestGroup.UNIT)
public class VectorFieldFirstOrderDifferentiatorTest {
private static final Function1D<DoubleMatrix1D, DoubleMatrix1D> F = new Function1D<DoubleMatrix1D, DoubleMatrix1D>() {
@Override
public DoubleMatrix1D evaluate(final DoubleMatrix1D x) {
final double x1 = x.getEntry(0);
final double x2 = x.getEntry(1);
final double[] y = new double[2];
y[0] = x1 * x1 + 2 * x2 * x2 - x1 * x2 + x1 * Math.cos(x2) - x2 * Math.sin(x1);
y[1] = 2 * x1 * x2 * Math.cos(x1 * x2) - x1 * Math.sin(x1) - x2 * Math.cos(x2);
return new DoubleMatrix1D(y);
}
};
private static final Function1D<DoubleMatrix1D, DoubleMatrix1D> F2 = new Function1D<DoubleMatrix1D, DoubleMatrix1D>() {
@Override
public DoubleMatrix1D evaluate(final DoubleMatrix1D x) {
final double x1 = x.getEntry(0);
final double x2 = x.getEntry(1);
final double[] y = new double[3];
y[0] = x1 * x1 + 2 * x2 * x2 - x1 * x2 + x1 * Math.cos(x2) - x2 * Math.sin(x1);
y[1] = 2 * x1 * x2 * Math.cos(x1 * x2) - x1 * Math.sin(x1) - x2 * Math.cos(x2);
y[2] = x1 - x2;
return new DoubleMatrix1D(y);
}
};
private static final Function1D<DoubleMatrix1D, DoubleMatrix2D> G = new Function1D<DoubleMatrix1D, DoubleMatrix2D>() {
@Override
public DoubleMatrix2D evaluate(final DoubleMatrix1D x) {
final double x1 = x.getEntry(0);
final double x2 = x.getEntry(1);
final double[][] jac = new double[2][2];
jac[0][0] = 2 * x1 - x2 + Math.cos(x2) - x2 * Math.cos(x1);
jac[0][1] = 4 * x2 - x1 - x1 * Math.sin(x2) - Math.sin(x1);
jac[1][0] = 2 * x2 * Math.cos(x1 * x2) - 2 * x1 * x2 * x2 * Math.sin(x1 * x2) - Math.sin(x1) - x1 * Math.cos(x1);
jac[1][1] = 2 * x1 * Math.cos(x1 * x2) - 2 * x1 * x1 * x2 * Math.sin(x1 * x2) - Math.cos(x2) + x2 * Math.sin(x2);
return new DoubleMatrix2D(jac);
}
};
private static final Function1D<DoubleMatrix1D, DoubleMatrix2D> G2 = new Function1D<DoubleMatrix1D, DoubleMatrix2D>() {
@Override
public DoubleMatrix2D evaluate(final DoubleMatrix1D x) {
final double x1 = x.getEntry(0);
final double x2 = x.getEntry(1);
final double[][] jac = new double[3][2];
jac[0][0] = 2 * x1 - x2 + Math.cos(x2) - x2 * Math.cos(x1);
jac[0][1] = 4 * x2 - x1 - x1 * Math.sin(x2) - Math.sin(x1);
jac[1][0] = 2 * x2 * Math.cos(x1 * x2) - 2 * x1 * x2 * x2 * Math.sin(x1 * x2) - Math.sin(x1) - x1 * Math.cos(x1);
jac[1][1] = 2 * x1 * Math.cos(x1 * x2) - 2 * x1 * x1 * x2 * Math.sin(x1 * x2) - Math.cos(x2) + x2 * Math.sin(x2);
jac[2][0] = 1;
jac[2][1] = -1;
return new DoubleMatrix2D(jac);
}
};
private static final Function1D<DoubleMatrix1D, Boolean> DOMAIN = new Function1D<DoubleMatrix1D, Boolean>() {
@Override
public Boolean evaluate(final DoubleMatrix1D x) {
final double x1 = x.getEntry(0);
final double x2 = x.getEntry(1);
if (x1 < 0 || x1 > Math.PI || x2 < 0 || x2 > Math.PI) {
return false;
}
return true;
}
};
private static final double EPS = 1e-5;
private static final VectorFieldFirstOrderDifferentiator FORWARD = new VectorFieldFirstOrderDifferentiator(FiniteDifferenceType.FORWARD, EPS);
private static final VectorFieldFirstOrderDifferentiator CENTRAL = new VectorFieldFirstOrderDifferentiator(FiniteDifferenceType.CENTRAL, EPS);
private static final VectorFieldFirstOrderDifferentiator BACKWARD = new VectorFieldFirstOrderDifferentiator(FiniteDifferenceType.BACKWARD, EPS);
@Test(expectedExceptions = IllegalArgumentException.class)
public void testNullDifferenceType() {
new ScalarFirstOrderDifferentiator(null);
}
@Test(expectedExceptions = IllegalArgumentException.class)
public void testNullFunction() {
CENTRAL.differentiate((Function1D<DoubleMatrix1D, DoubleMatrix1D>) null);
}
@Test
public void test() {
final DoubleMatrix1D x = new DoubleMatrix1D(new double[] {.2245, -1.2344 });
final DoubleMatrix2D anJac = G.evaluate(x);
final DoubleMatrix2D fdFwdJac = FORWARD.differentiate(F).evaluate(x);
final DoubleMatrix2D fdCentGrad = CENTRAL.differentiate(F).evaluate(x);
final DoubleMatrix2D fdBackGrad = BACKWARD.differentiate(F).evaluate(x);
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) {
assertEquals(fdFwdJac.getEntry(i, j), anJac.getEntry(i, j), 10 * EPS);
assertEquals(fdCentGrad.getEntry(i, j), anJac.getEntry(i, j), 10 * EPS * EPS);
assertEquals(fdBackGrad.getEntry(i, j), anJac.getEntry(i, j), 10 * EPS);
}
}
}
@Test
public void test2() {
final DoubleMatrix1D x = new DoubleMatrix1D(new double[] {1.3423, 0.235 });
final DoubleMatrix2D anJac = G2.evaluate(x);
final DoubleMatrix2D fdFwdJac = FORWARD.differentiate(F2).evaluate(x);
final DoubleMatrix2D fdCentGrad = CENTRAL.differentiate(F2).evaluate(x);
final DoubleMatrix2D fdBackGrad = BACKWARD.differentiate(F2).evaluate(x);
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 2; j++) {
assertEquals(fdFwdJac.getEntry(i, j), anJac.getEntry(i, j), 10 * EPS);
assertEquals(fdCentGrad.getEntry(i, j), anJac.getEntry(i, j), 10 * EPS * EPS);
assertEquals(fdBackGrad.getEntry(i, j), anJac.getEntry(i, j), 10 * EPS);
}
}
}
@Test(expectedExceptions = IllegalArgumentException.class)
public void outsideDomainTest() {
final Function1D<DoubleMatrix1D, DoubleMatrix2D> fdJacFunc = CENTRAL.differentiate(F2, DOMAIN);
fdJacFunc.evaluate(new DoubleMatrix1D(2.3, 3.2));
}
@Test
public void testDomain() {
final DoubleMatrix1D[] x = new DoubleMatrix1D[7];
x[0] = new DoubleMatrix1D(new double[] {1.3423, 0.235 });
x[1] = new DoubleMatrix1D(new double[] {0.0, 1.235 });
x[2] = new DoubleMatrix1D(new double[] {Math.PI, 3.1 });
x[3] = new DoubleMatrix1D(new double[] {2.3, 0.0 });
x[4] = new DoubleMatrix1D(new double[] {2.3, Math.PI });
x[5] = new DoubleMatrix1D(new double[] {0.0, 0.0 });
x[6] = new DoubleMatrix1D(new double[] {Math.PI, Math.PI });
final Function1D<DoubleMatrix1D, DoubleMatrix2D> fdJacFunc = CENTRAL.differentiate(F2, DOMAIN);
for (int k = 0; k < 7; k++) {
final DoubleMatrix2D anJac = G2.evaluate(x[k]);
final DoubleMatrix2D fdJac = fdJacFunc.evaluate(x[k]);
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 2; j++) {
assertEquals("set " + k, anJac.getEntry(i, j), fdJac.getEntry(i, j), 1e-8);
}
}
}
}
}